"growing familiarity" is a correct and usable phrase in written English.
You can use it to describe an increasing level of understanding between two people, places, or things. For example, "The growing familiarity between the two companies was key to their successful partnership."
The benefit of using the same questions resides in the audience's growing familiarity with them.
He wants to record every detail of his growing familiarity with the family.
Five years of growing familiarity with the Tories have bred some cold contempt.
In The New Yorker, Pankaj Mishra dismissed Ms. Hirsi Ali's "simple oppositions" and "growing familiarity with right-wing touchstones".
The company hopes to capitalize on the growing familiarity with food trucks, said Jessica Jackson, the group head of public relations and communications at Heinz North America.
Her praise for the United States, her new home, shows a growing familiarity with right-wing touchstones (self-reliance, distrust of government, family values, gun ownership, Christianity).
I found myself in the privileged position of being able to discover how children and animals interacted, how growing confidence and familiarity banished anxiety.
And what is so intriguing is that the majority of these insights into women's rights, urban poverty, prostitution, drug addiction, bureaucratic incompetence, legal intransigence and the growing student fascination and familiarity with outside ideas and new technologies have been granted export licences by a regime that is supposedly stricter than Poland's pre-glasnost communists.
Things that had grown stale from familiarity now drew his attention.
Their blend of 1960s pop, indie aesthetics and acid-house beats, though initially dazzling, has grown bland with familiarity.
What we're seeing instead is authority wedges forming as new platform novelty tails off and familiarity grows.
